| Euclides - 1840
...by the parts. F T» PROP. IV. THEOR. If a straight line (AB) be divided into any two parts (AF, FB), **the square of the whole line is equal to the squares of the** parts, together with twice the rectangle contained by the parts. Upon AB describe the square ACDB ;... | |
| John M'Nevin - Arithmetic - 1841 - 280 pages
...like manner 22 = 2 x 10 = 20+ 2 = 2 tens and 2 over. Hence, from the properties of Euclid. 4, Lib. 2. **"If a straight line be divided into any two parts...with twice the rectangle contained by the parts."** Thus, let AB be divided into two parts, 6 equal to 6 squared plus 4 squared, together with twice the... | |
| John M'Nevin - Arithmetic - 1841 - 280 pages
...like manner 22 = 2 x 10= 20 + 2 = 2 tens and 2 over. Hence, from the properties of Euclid. 4, Lib. 2. **"If a straight line be divided into any two parts...with twice the rectangle contained by the parts."** Thus, let AB be divided into two parts, 6 and 4, the square of the whole line 10, which is 100, is... | |
| Jeremiah Day - Algebra - 1841 - 332 pages
...than in ordinary language. The proposition, (Euc. 4. 2.) that when a straight line is divided into **two parts, the square of the whole line is equal to the squares of the two parts, together with** tv/ice the product of the parts, is demonstrated, by involving a binomial. Let the side of a square... | |
| Euclides - Geometry - 1841 - 351 pages
...twice the rectangle contained by the whole and that part, together with the square of the otherpart. **Let the straight line AB be divided into any two parts in** the point C; the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the... | |
| William Grier - Mechanical engineering - 1842 - 308 pages
...and AE, and AD and EF, and AD and FB: thus expressed, AD . AB=AD . AE +AD . EF+AD . FB.* If a right **line be divided into any two parts, the square of the whole line, is equal to** both the rectangles of the whole line and each of the parts. 30. Let the line AB be the sum of any... | |
| Euclides - 1842
...rectangles contained by the whole and each of the parts, are together equal to the square of the whole fine. **Let the straight line AB be divided into any two parts in** the point c ; the rectangle contained by AB, BC, together with the rectangle* AB, AC, shall be equal... | |
| John Playfair - Euclid's Elements - 1842 - 317 pages
...contained by the whole and each of the parts, are together equal to the square of the whole line. F c B **Let the straight line AB be divided into any two parts in** the point C ; the rectangle AB.BC, together with the rectangle AB.AC, is equal to the square of AB... | |
| Scotland free church, gen. assembly - 1847
...two right angles. 3. Parallelograms upon equal bases, and between the same parallels, are equal. 4. **If a straight line be divided into any two parts,...square of the whole line is equal to the squares of** each of the parts together with twice the rectangle contained by the parts. 5. Equal straight lines... | |
| James Bates Thomson - Algebra - 1844 - 252 pages
...than in ordinary language. The proposition, (Euc. 4. 2,) that when a straight line is divided into **two parts, the square of the whole line is equal to...squares of the two parts, together with twice the** product of the parts, is demonstrated, by involving a binomial. •..-••' Let the side of a square... | |
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